Understanding IS-LM Model in Keynesian Economics

1. Unit 4: Money and National Income Keynes proposed that low aggregate demand is responsible for the low income and high unemployment that characterize economic downturns. He criticized classical theory for assuming that aggregate supply alone—capital, labour, and technology—determines national income. Economists today reconcile these two views with the model of aggregate demand and aggregate supply.

2. IS – LM model IS-LM model The goal of the IS-LM model is to show what determines national income for a given price level. There are two ways to interpret this exercise. We can view the IS–LM model as showing what causes income to change in the short run when the price level is fixed because all prices are sticky. Or we can view the model as showing what causes the aggregate demand curve to shift.

3. IS – LM model (Cont.) IS stands for “investment’’ and “saving,’’ and the IS curve represents what’s going on in the market for goods and services. LM stands for “liquidity’’ and “money,’’ and the LM curve represents what’s happening to the supply and demand for money. Because the interest rate influences both investment and money demand, it is the variable that links the two halves of the IS–LM model. The model shows how interactions between the goods and money markets determine the position and slope of the aggregate demand curve and, therefore, the level of national income in the short run.

4. The Goods Market and the IS Curve Keynesian Cross In The General Theory Keynes proposed that an economy’s total income was, in the short run, determined largely by the spending plans of households, businesses, and government. The more people want to spend, the more goods and services firms can sell. The more firms can sell, the more output they will choose to produce and the more workers they will choose to hire. Keynes believed that the problem during recessions and depressions was inadequate spending.

5. The Goods Market and the IS Curve (Cont.) The Interest Rate, Investment, and the IS Curve. Planned investment depends on the rate of interest, r. I = I(r) Interest rate is the cost of borrowing to finance investment projects. An increase in the interest rate reduces planned investment. As a result, the investment function slopes downward.

6. The Investment function • The investment function shows that an increase in the interest rate from r1 to r2 reduces planned investment from I(1) to I(2). • I = c-d(r) The Goods Market and the IS Curve (Cont.) Interest rate r2 r1 I I2 I1 Investment

7. The Investment function • The IS curve shows that an increase in the interest rate from r1 to r2 reduces income from Y(1) to Y(2). The Goods Market and the IS Curve (Cont.) Interest rate Interest rate r2 r2 r1 r1 I2 I1 Y2 Y1 Investment Income

8. The IS Curve • The IS curve: • Y = C + I + G • Where: • C = a + b (Yd) • I = c – d(r) • G = G’ Interest rate The Goods Market and the IS Curve (Cont.) Increase in govt. spending • The economy is assumed to be closed IS1 IS2 Income

9. The IS curve: • Y = C + I + G • Where: • C = a + b (Yd); I = c – d(r) ; G = G’ • So: Y = a + b(Y-T) + c – d(r) +G’ • Y –bY = a – bT + c – d(r) +G’ • Y = [a –bT + c – d(r) + G’] / (1-b) • There is a negative relationship between income and the interest rate • When the interest rate increases, income decreases. The Goods Market and the IS Curve (Cont.)

10. The Goods Market and the IS Curve (Cont.) How Fiscal Policy shifts the IS Curve: The IS curve shows us, for any given interest rate, the level of income that brings the goods market into equilibrium. As we learned from the Keynesian cross, the equilibrium level of income also depends on government spending G and taxes T. The IS curve is drawn for a given fiscal policy; that is, when we construct the IS curve, we hold G and T fixed. When fiscal policy changes, the IS curve shifts.

11. The Goods Market and the IS Curve (Cont.) How Fiscal Policy Shifts the IS Curve: An Increase in Government spending shifts the IS curve outward (to the right) - an increase in government purchases raises planned expenditure. For any given interest rate, the upward shift in planned expenditure of ΔG leads to an increase in income Y of ΔG/(1 − MPC). The IS curve shifts to the right by this amount.

12. The Goods Market and the IS Curve (Cont.) In summary, the IS curve shows the combinations of the interest rate and the level of income that are consistent with equilibrium in the market for goods and services (in the short-run). The IS curve is drawn for a given fiscal policy. Changes in fiscal policy that raise the demand for goods and services shift the IS curve to the right. Changes in fiscal policy that reduce the demand for goods and services shift the IS curve to the left.

13. The Goods Market and the IS Curve (Cont.) Note: IS = C + I + G Y = a + b(Y-T) + c – d(r) +G’ Any changes to C’ , I’ , G’ or T will cause the IS curve to shift (left or right) A change to the interest rate, r, or to income, Y, will cause a movement along the IS curve A change to b or d will cause a change in the Multiplier

14. The Money Market and the LM Curve • The LM curve plots the relationshipbetween the interest rate and the level of income that arises in the market for money balances. The Theory of Liquidity Preference • The theory of liquidity preference assumes there is a fixed supply of real money balances, That is: Real Money supply = Nominal money balance / Price level

15. The Money Market and the LM Curve (Cont.) • The money supply M is an exogenous policy variable chosen by a central bank. • The price level P is also an exogenous variable in this model. (We take the price level as given because the IS–LM model explains the short run when the price level is fixed). • These assumptions imply that the supply of real money balances is fixed and, in particular, does not depend on the interest rate. • Ms’ = (M/P)

16. The Money Market and the LM Curve (Cont.) • The theory of liquidity preference state that the interest rate is one determinant of how much money people choose to hold. • The underlying reason is that the interest rate is the opportunity cost of holding money: it is what you forgo by holding some of your assets as money, which does not bear interest, instead of as interest-bearing bank deposits or bonds. • When the interest rate rises, people want to hold less of their wealth in the form of cash / money. We can write the demand for real money balances as: Md = L(r), where money demand is negatively related to interest rate

17. The Money Market and the LM Curve (Cont.) • The supply and demand for real money balances determine the interest rate. • The supply curve for real money balances is vertical because the supply does not depend on the interest rate. • The demand curve is downward sloping because a higher interest rate raises the cost of holding money and thus lowers the quantity demanded. • At the equilibrium interest rate, the quantity of real money balances demanded equals the quantity of real money balance supplied.

18. The Money Market and the LM Curve (Cont.) The money market equilibrium Interest rate Ms = M/P r Md = l(r) Real money balance

19. The Money Market and the LM Curve (Cont.) • How does the interest rate get to this equilibrium of money supply and money demand? • The adjustment occurs because whenever the money market is not in equilibrium, people try to adjust their portfolios of assets and, in the process, alter the interest rate. • For instance, if the interest rate is above the equilibriumlevel, the quantity of real money balances supplied exceeds the quantity demanded. • Individuals holding the excess supply of money try to convert some of their non-interest-bearing money into interest-bearing bank deposits or bonds.

20. The Money Market and the LM Curve (Cont.) • Banks and bond issuers, who prefer to pay lower interest rates, respond to this excess supply of money by lowering the interest rates they offer. • Conversely, if the interest rate is below the equilibrium level, so that the quantity of money demanded exceeds the quantity supplied, individuals try to obtain money by selling bonds or making bank withdrawals. • To attract now scarcer funds, banks and bond issuers respond by increasing the interest rates they offer. • The interest rate reaches the equilibrium level where which people are content with their portfolios of monetary and nonmonetary assets.

21. The Money Market and the LM Curve (Cont.) Interest rate Interest rate • The higher Y, the higher Md (increase in transactions) – LM curve is upward sloping Ms LM = M/P = L(r,Y) r3 Md3 r2 Md2 r1 Md1 Y1 Y2 Y3 Real money balance Income

22. The Money Market and the LM Curve (Cont.) • The LM curve summarizes this relationship between the level of income and the interest rate. • Each point on the LM curve represents equilibrium in the money market, and the curve illustrates how the equilibrium interest rate depends on the level of income. • The higher the level of income, the higher the demand for real money balances, and the higher the equilibrium interest rate. • For this reason, the LM curve slopes upward.

23. Income, Money Demand, and the LM Curve (Cont.) How does a change in the economy’s level of income Y affect the market for real money balances? • The level of income effects the demand for money. When income is high, expenditure is high, so people engage in more transactions that require the use of money. • Thus, greater income implies greater money demand. We can express these ideas by writing the money demand function as: (M/P)d = L(r, Y). • The quantity of real money balances demanded is negatively related to the interest rate and positively related to income. LM: Increase in Y = increase in Md = increase in r IS: Increase in r = decrease in I = decrease in Y

24. Income, Money Demand, and the LM Curve What happens to the equilibrium interest rate when the level of income changes? • For example, consider what happens in when income increases from Y1 to Y2. • This increase in income shifts the money demand curve to the right. With the supply of real money balances unchanged, the interest rate must rise from r1 to r2 to equilibrate the money market. • Therefore, according to the theory of liquidity preference, higher income leads to a higher interest rate.

25. Income, Money Demand, and the LM Curve (Cont.) How Monetary Policy Shifts the LM Curve • Let us use the theory of liquidity preference to understand how monetary policy shifts the LM curve. • Suppose that the Bank of Namibia decreases the money supply from M1 to M2, which causes the supply of real money balances to fall from M1/P to M2/P. • Holding constant the amount of income and thus the demand curve for real money balances, we see that a reduction in the supply of real money balances raises the interest rate that equilibrates the money market. • Hence, a decrease in the money supply shifts the LM curve upward.

26. Income, Money Demand, and the LM Curve (Cont.) • In summary: the LM curve shows the combinations of the interest rate and the level of income that are consistent with equilibrium in the market for real money balances. • The LM curve is drawn for a given supply of real money balances. • Decreases in the supply of real money balances shift the LM curve upward / to the left. • Increases in the supply of real money balances shift the LM curve downward / to the right. • Changes in Y or r cause a movement along the LM curve. What if CB rather changed r?

27. The short-run equilibrium We now have all the pieces of the IS–LM model. • The two equations of this model are: • IS: Y = C(Y − T) + I(r) +G • LM: M/P = L(r, Y ) • The model takes fiscal policy G and T, monetary policy M, and the price Level P as exogenous. • Given these exogenous variables, the IS curve provides the combinations of r and Y that satisfy the equation representing the goods market. • The LM curve provides the combinations of r and Y that satisfy the equation representing the money market.

28. The short-run equilibrium (Cont.) IS-LM equilibrium Interest rate • The good and money markets are both in equilibrium at Ye. LM re IS Income Ye

29. The short-run equilibrium (Cont.) A numerical example to practice Consider the following short-run model of closed economy: Good Market C=10+0.1Yd I = 5-5r G = 20; T = 10 Money Market M = 10 P = 2 L(Y,r) = Y –r

30. The short-run equilibrium (Cont.) A numerical example to practice We will start by constructing IS and LM equation IS equation: Y = C(Y − T) + I(r) +G Y = 10 + 0.1(Y-10) +5-5r+ 20 Y = 10 + 0.1Y -1 + 5 – 5r +20 0.9Y = 34 – 5r Y = 37.8 – 5.6 r

31. The short-run equilibrium (Cont.) A numerical example to practice We will start by constructing IS and LM equation LM equation: Y –r = M/P = 5 Y = 5 + r

32. The short-run equilibrium (Cont.) A numerical example to practice Now we equate IS and LM Y = 37.8 – 5.6 r = 5 + r 32.8 = 6.6 r r = 4.9% Y = 9.9

33. Fiscal policy in the IS-LM model • The government implements a fiscal expansion policy (increase in G or decrease in T) • The IS curve shifts to the right • This results in an increase in Y and an increase in r Fiscal expansion r LM r2 r1 IS2 IS1 Y Y1 Y2

34. Monetary policy in the IS-LM model • The government implements a monetary expansion policy (Increase in Ms or decrease in r) • The LM curve shifts to the right / down • This results in an increase in Y and a decrease in r Monetary expansion r LM1 LM2 r1 r2 IS Y Y1 Y2

35. The AD-AS model • The AD Model: All P,Y combinations such that IS=LM, so that both the goods and money markets are in equilibrium. • In the AD-AS model, prices are flexible • Together, the goods and money markets constitute the demand side of the economy. • The major difference between the IS/LM model and the AD model is their treatments of P: in the IS/LM model, P is exogenous; in the AD model, P is endogenous. • IS/LM model is a short-run model where P is fixed, AS-AS model is a medium-term model where P can vary

36. The AD-AS model (Cont.) • The AD Model is derived from the IS-LM model. • AD: A reduction in price (through the money market) leads to an increase in income Interest rate Price level LM1 LM2 Aggregate demand r1 p1 p2 r2 IS Y1 Y2 Y1 Y2 Income Income

37. The AD-AS model (Cont.) • The equation for the AD curve is: • Y = Y(M/P, G, T, Z) • Where Y is real GDP, M is the nominal money supply, P is the price level, G is real government spending, T is an exogenous component of real taxes levied, and Z1 is the other exogenous variables that affect the IS curve or the LM. • The real money supply has a positive effect on aggregate demand, as does real government spending. • The exogenous component of taxes has a negative effect on it.

38. The AD-AS model (Cont.) • The equation for the AS curve is: • Y = Y(W/P; P, X) • W is the nominal wage rate P is the price level, and X is the exogenous variables that can affect the position of the labour demand curve (the capital stock or the current state of technological knowledge). • The real wage has a negative effect on firms' employment of labour and thus decreases aggregate supply. • The price level has a positive effect on aggregate supply as it induces increases in production.

39. The AD-AS model (Cont.) • Fiscal expansion would shift out the AD curve, resulting in an increase in Y and P AD-AS equilibrium: Price level AS P2 P1 AD2 AD1 Y1 Y2 Output / Income

40. Phillips curve Phillips curve • The Phillips curve describes an inverse relationship between rates of unemployment and corresponding rates of inflation that result within an economy. E.g. decreased unemployment results in higher rates of inflation. • While there is a short run trade-off between unemployment and inflation, it has not been observed in the long-run. • There can be low unemployment and low inflation (economic development). • There can be high unemployment and high inflation (stagflation). Inflation Unemployment Short-run vs. long run theories Classical vs. Keynesian theories